Nonparametric Modeling and Prognosis of Condition Monitoring Signals Using Multivariate Gaussian Convolution Processes

ABSTRACT

Condition monitoring (CM) signals play a critical role in assessing the remaining useful life of in-service components. In this article, an alternative view on modeling CM signals is proposed. This view draws its roots from multitask learning and is based on treating each CM signal as an individual task. Each task is then expressed as a convolution of a latent function drawn from a Gaussian process (GP), and the transfer of knowledge is achieved through sharing these latent functions between historical and in-service CM signals. Aside from being nonparametric, the flexible and individualistic approach in our model can account for heterogeneity in the data and automatically infer the commonalities between the new testing observations and CM signals in the historical dataset. The robustness and advantageous features of the proposed method are demonstrated through numerical studies and a case study with real-world data in the application to find the remaining useful life prediction of automotive lead-acid batteries. Technical details and additional numerical results are available in the supplementary materials.

KEYWORDS:

• Condition monitoring signals
• Convolution process
• Multitask learning
• Multivariate Gaussian process
• Remaining useful life

Supplementary Materials

Appendix A.1: Covariance Function: A detailed derivation of (8) is provided.

Appendix A.2: Gaussian Based Covariance: A detailed derivation of the convolved covariance function in (10) is provided.

Appendix A.3: Computational Complexity: The computational complexity of our model is derived based on likelihood factorization.

Appendix A.4: Computational Simplifications and MLE Estimation: Simplifications and guidelines for likelihood calculation and MLE estimation are provided.

Appendix A.5: Computational Comparisons: A computational comparison is provided based on Model Setting IV.

Appendix A.6: Remaining Useful Life Distribution: A detailed derivation of the RUL distribution is provided.

Appendix A.7: Extension to Multiple In-Service Units: An extension of our model for simultaneous prediction of multiple in-service units is provided.

Appendix A.8: Sensitivity Studies: Sensitivity analysis based on sparse data and low failure probability is provided.

Acknowledgments

The authors thank the editors and reviewers for their constructive comments and suggestions on this article.

This research was supported by the National Science Foundation under grant numbers 1335129 and 1343969.